It is common knowledge that music can evoke emotions. But how do these emotions arise and how does meaning emerge in music? Almost 70 years ago, music philosopher Leonard Meyer suggested that both are due to an interplay between expectation and surprise. In the course of evolution, it was crucial for humans to be able to make new predictions based on past experiences. This is how we can also form expectations and predictions about the progression of music based on what we have heard. According to Meyer, emotions and meaning in music arise from the interplay of expectations and their fulfillment or (temporary) non-fulfillment.
A team of scientists led by Theo Geisel at the MPI-DS and the University of Göttingen have asked themselves whether these philosophical concepts can be quantified empirically using modern methods of data science. In a paper published recently in Nature Communications, they used time series analysis to infer the autocorrelation function of musical pitch sequences; it measures how similar a tone sequence is to previous sequences. This results in a kind of "memory" of the piece of music. If this memory decreases only slowly with time difference, the time series is easier to anticipate; if it vanishes rapidly, the time series offers more variation and surprises.
In total, the researchers Theo Geisel and Corentin Nelias analyzed more than 450 jazz improvisations and 99 classical compositions in this way, including multi-movement symphonies and sonatas. They found that the autocorrelation function of pitches initially decreases very slowly with the time difference. This expresses a high similarity and possibility to anticipate musical sequences. However, they found that there is a time limit, after which this similarity and predictability ends relatively abruptly. For larger time differences, the autocorrelation function and memory are both negligible.
